This invention relates generally to determining the yield point, also known as yield stress, of a fluid as well as conventional shear stress versus shear rate viscosity data. More particularly, this invention relates to adapting a conventional bob and sleeve viscometer to provide direct measurement of a material's yield stress.
Ascertaining rheological properties of fluids used in drilling and completing oil and gas wells normally requires that “shear stress-shear rate” data (referred to as “rheogram data”) be collected via a viscometric device. Then by selecting an a priori viscosity model, the data can be analyzed, usually by statistical means, to determine “best fit” model parameters that are the quantitative estimates for specific rheological properties, including yield stress. Common models used in the oil and gas industry include:
Newtonian fluid, defined as:                     μ        =                              [                          τ              γ                        ]                    =          constant                                    [        1        ]            
Power Law, defined as:                               η          PL                =                              [                          τ              γ                        ]                    =                                                    K                p                            ⁡                              (                                  γ                  .                                )                                                                    n                p                            -              1                                                          [        2        ]            
Bingham Plastic, defined as:                               η          BP                =                              [                          τ                              γ                .                                      ]                    =                                    [                              YP                                  γ                  .                                            ]                        +            PV                                              [        3        ]            
Herschel-Bulkley, defined as:                               η          HB                =                              [                          τ                              γ                .                                      ]                    =                                    [                                                τ                  0                                                  γ                  .                                            ]                        +                                                            K                  HB                                ⁡                                  (                                      γ                    .                                    )                                                                              n                  H                                -                1                                                                        [        4        ]            
Robertson-Stiff, defined as:                               η          RS                =                              [                          τ                              γ                .                                      ]                    =                                    [                                                A                  ⁡                                      (                                          C                      +                                              γ                        .                                                              )                                                  B                            ]                                      γ              .                                                          [        5        ]            where: η=apparent viscosity; τ=viscometric shear stress; γ=viscometric shear rate; μ=Newtonian viscosity coefficient; ηPL=apparent viscosity for power law model; Kp=power law consistency coefficient=apparent viscosity at shear rate of unity; np=power law shear thinning index; ηBP=apparent viscosity for Bingham Plastic model; YP=Bingham Plastic yield point; PV=Bingham Plastic viscosity coefficient; ηHB=apparent viscosity for Herschel-Bulkley model; KHB=Herschel-Bulkley consistency coefficient; nH=Herschel-Bulkley shear thinning index; τ0=yield stress or yield point for Herschel-Bulkley fluid; ηRS=apparent viscosity for Robertson-Stiff model, and A, B and C are coefficients for the Robertson-Stiff model. Note that the quantity A(C)B equates to the yield stress of the material.
In most cementing applications and many drilling fluids, it is necessary to deploy a rheological model that accommodates a finite “yield stress”, often referred to as the yield point (YP). The YP is the threshold shear stress that must be applied to create flow of a fluid. Yield stress or yield point of drilling muds and cementing fluids directly affects their performance. For example, yield stress/yield point of a fluid directly impacts the conditions under which laminar flow becomes turbulent. For a drilling mud, it relates to the mud's ability to transport cuttings from the wellbore, for example. In cementing fluids, it relates to the fluid's ability to remove “mud cake” and control gas migration, for example.
The most common viscometer configuration used in measuring rheology of drilling and oil/gas completion fluids is a simple concentric cylinder viscometer (Couette).
Referring to FIG. 1, such a viscometer has an outer cylinder 2, called the “sleeve,” with a concentric inner cylinder 4, called the “bob.” The sleeve 2 fits concentrically around the outside of the bob 4, leaving a small annular gap 6 in which the fluid sample is received. The sleeve 2 attaches to a motor-driven rotating drive collar (generally shown as motor drive 8) that turns the sleeve 2 at a predetermined rotational speed. In many cases, the bob 4 is a cylinder that has a rod or stem 10 extending from the top. The stem 10 is inserted into a receptacle device that measures torque. The receptacle device of one type of rotating viscometer includes a spring 12. Such a viscometer correlates displacement of the spring 12 caused by rotation of the attached bob 4 with torque being applied to the bob 4 by the fluid sample to which stress is applied by the motor-driven sleeve 2. Torque is indicated by a suitable torque readout, such as a torque dial 14, for example.
In use, the bob/sleeve assembly is lowered into a sample of material until the fluid sample fills a pre-designated portion of the annular gap 6 (the volumetric space between the bob 4 and sleeve 2 over some specified axial distance). A rotational speed is selected and the motor of the motor drive 8 is turned on. The rotating drive collar turns the sleeve 2, which applies a stress to the fluid in the annular gap 6. If the stress is sufficient, the fluid will flow in the rotational direction, applying a resulting stress to the bob 4. The stress applied to the outer surface of the bob 4 creates a torque on the bob 4. This torque is transferred to the spring 12, which moves the viscometer's torque dial 14 that is calibrated in torque units.
Known mathematical formulas can be used in known manner to transform the dimensions of the bob 4 and sleeve 2, along with the rotational speed of the sleeve 2 and the corresponding torque measured by the bob 4 as shown on the torque dial 14, into a set of shear stress and shear rate data.
There are two methods for determining the YP of a fluid: one (called RF, regression fit) is to select a viscosity model a priori, and statistically determine the best fitting parameters; the other method is often referred to as “direct measurement” (DM). In the RF method, a model such as Equation [3], [4] or [5] above is selected, and then statistical regression used to best fit that model to the rheogram data. The American Petroleum Institute (API) has recommended practices for using shear stress and shear rate data for a fluid to ascertain rheological characteristics or parameters, including the yield stress (also referred to as yield point) and plastic viscosity of a Bingham Plastic fluid model. However, the value of YP obtained by curve fitting a predetermined model via a given set of shear stress and shear rate data depends upon which model was selected. Herein lies the problem. The actual yield stress of a fluid is a physical property, and yet common practice in the industry is to transform shear stress and shear rate data into a best fit (regressed) value for yield point. With complex oil field cementing systems, for example, this method can often result in significant error.
Thus, the DM method is preferred over the RF method. The DM method usually requires very sensitive speed control and torque measuring sensors. The DM method can be further partitioned into two general categories: the YP,i method, being the minimal shear stress required to initiate flow when starting from a stationary condition; while the YP,e method is aimed at measuring the equilibrium stress state that a fluid retains as it comes to rest, after turning off the rotation of the moving cylinder. The YP,i method usually entails measuring the torque versus time profile while starting a viscometer from the “rest position;” this usually requires the ability to rotate the sleeve very slowly, often less than one revolution per minute (rpm). The YP,e method requires the torque decay curve to be carefully monitored after turning off the rotating cylinder. The rotating cylinder will come to rest while the fluid retains an internal stress that is equal to the YP. Due to inertial effects, the rotational speed of both DM methods (YP,i and YP,e) should be below one revolution per minute for most of the oil field type Couette viscometers. These conventional oil field viscometers are, however, not sufficiently sensitive to measure the low torque values for either DM method. Additionally, these field viscometers may not be equipped with the capability of controlling a constant rotational speed less than unity. Error can also be induced by slippage that occurs between the smooth surface of a bob and the fluid, especially when particulates are present. This slippage may cause significant error when measured torques are quite low. To overcome this problem, a vane device (reference page 138 of J. F. Steffe, Rheological Methods in Food Process Engineering (1992)), shown in FIGS. 2A and 2B, is often used as an accepted method among those skilled in the art. The purpose of the vanes is to create an “inner cylinder” or bob out of the fluid sample, thus the shearing interface between the bob and sleeve is “fluid-to-fluid”, rather than “metal-to-fluid.”
FIGS. 2A and 2B represent a ten-bladed vane device 16 for directly measuring YP by either the YP,i method or the YP,e method. The vane device 16 connects to the torque sensor of a rotational viscometer and is lowered into the fluid sample as described above for the Couette or rotating viscometer of FIG. 1. In the YP,i method, the rotational speed is set very low (usually less than or equal to one rpm), then the switch is turned on, and torque versus time is monitored until the torque peaks, as shown in FIG. 3A at 18a. The peak torque is converted into a shear stress being applied to the effective circumferential area of the vane's fluid-to-fluid interface using vane device 16. The yield point is computed from the peak torque 18a observed in FIG. 3A, which represents the stress required to initiate flow. The subsequent decline in torque shown by the graph in FIG. 3A implies that flow has been initiated. In the YP,e method, the vane device 16 connects to the torque sensor of a rotational viscometer and is lowered into the fluid sample as described above for the Couette or rotating viscometer of FIG. 1. The rotational speed is set very low (less than or equal to one rpm), then the switch is turned on, and the vane (bob) or sleeve rotates at constant rpm creating a torque versus time curve shown in FIG. 3B. Once equilibrium has been obtained, usually indicated by a constant level or torque, such as line 18b, the device is turned off and the torque versus time decay is recorded, as 18c and 18d observed in FIG. 3B. To ensure that the inertial effects have not significantly contributed to the torque readings in the YP,i and YP,e methods, a common analysis method is to plot the YP,i and YP,e torques, 18a and 18d, respectively, versus three or four of the lowest rotational speeds obtainable, as shown in FIG. 3C. The torque versus rotational speed data should approach an asymptotic value as speed approaches zero, see 18e in FIG. 3C. The asymptote 18e is the torque value to use to compute YP.
However, conventional oil field Couette viscometers have three limitations that prevent their use with a vane device for measuring yield stress: their torque responsive springs are not sensitive enough for accurate detection; many such viscometers are not equipped with capabilities of operating at less than one rpm; and the vane device works best if it is attached to a rotating shaft and lowered into a large sample of fluid, without the use of the outer sleeve. Most oil field viscometers are equipped with their rotational devices connected to the outer cylinder (the sleeve), while the inner cylinder (the bob) remains stationary and connected to the torque spring, as observed in FIG. 1. When attempts were made to adapt the vane in FIGS. 2A and 2B to a typical oil field viscometer, the device was not sensitive enough to detect low levels of YP, such as less than ten pascals (Pa). The problem is the combination of sensitivity of the torque spring and the fact that the vane remains stationary, while the sleeve rotates.
In the case of cements with added particulates and fracturing fluids with proppant, conventional Couette viscometers are not normally capable of accurately measuring rheogram data nor YP due to two key constraints: the, gap between the bob and sleeve is too small, thus particles easily jam and lock-up the viscometer; and the rotation of the sleeve creates centrifugal forces that cause the particles to migrate and stratify in the radial direction. Both of these physical phenomena cause unacceptable error.
Therefore, a device is needed that could readily adapt to conventional oil field Couette type viscometers for providing capabilities to accurately and directly measure YP, as well as rheogram data (shear stress versus shear rate data) for fluids with particles. There is also the need for a simple device that could readily adapt to the current oil field viscometer and measure rheology of particle laden fluids, especially yield stress (yield point) data.